Ordinary Differential Equations and Mechanical Systems
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Beschreibung
This book applies a step-by-step treatment of the current state-of-the-art of ordinary differential equations used in modeling of engineering systems/processes and beyond. It covers systematically ordered problems, beginning with first and second order ODEs, linear and higher-order ODEs of polynomial form, theory and criteria of similarity, modeling approaches, phase plane and phase space concepts, stability optimization, and ending on chaos and synchronization.
Presenting both an overview of the theory of the introductory differential equations in the context of applicability and a systematic treatment of modeling of numerous engineering and physical problems through linear and non-linear ODEs, the volume is self-contained, yet serves both scientific and engineering interests. The presentation relies on a general treatment, analytical and numerical methods, concrete examples, and engineering intuition.
The scientific background used is well balanced between elementary and advanced level, making it as a unique self-contained source for both theoretically and application oriented graduate and doctoral students, university teachers, researchers and engineers of mechanical, civil and mechatronic engineering.
This book applies a step-by-step treatment of the current state-of-the-art of ordinary differential equations used in modeling of engineering systems/processes and beyond. It covers systematically ordered problems, beginning with first and second order ODEs, linear and higher-order ODEs of polynomial form, theory and criteria of similarity, modeling approaches, phase plane and phase space concepts, stability optimization and ending on chaos and synchronization.
Presenting both an overview of the theory of the introductory differential equations in the context of applicability and a systematic treatment of modeling of numerous engineering and physical problems through linear and non-linear ODEs, the volume is self-contained, yet serves both scientific and engineering interests. The presentation relies on a general treatment, analytical and numerical methods, concrete examples and engineering intuition.
The scientific background used is well balanced between elementary and advanced level, making it as a unique self-contained source for both theoretically and application oriented graduate and doctoral students, university teachers, researchers and engineers of mechanical, civil and mechatronic engineering.
Contains a diverse selection of chapters, ranging from the first and the second order ODEs to bifurcation to modeling Richly illustrates each chapter with a number of examples that don't depend on a particular choice of computer-based methods Emphasizes the importance and benefits of mathematical modeling of physical and engineering objects through ordinary differential equations
Autor*in
Jan Awrejcewicz
Themen in »Ordinary Differential Equations and Mechanical Systems«
Hamiltonian systems Jacobi-Levi-Civita equation Krylov method Legendre equation Peano and Cauchy-Picard theorem double Hopf bifurcation ordinary differential equations
Stimmen zu »Ordinary Differential Equations and Mechanical Systems«
“The book is a welcome addition to the vast collection of ODE books – particularly for graduate students and researchers needing to obtain more insight than is available through routine numerical solutions. … the book should be well-received by researchers and by libraries where it is likely to be a sought after reference for years to come.” (Ronald L. Huston, zbMATH 1308.34001, 2015)
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